Roy-Steiner equations for pion-nucleon scattering

Abstract

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high-energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the $\pi \pi \to \bar{N}N$ partial waves into the form of a Muskhelishvili-Omnès problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.

106 pages, 18 figures; version published in JHEP

References in corpus (27)

• Roy equation analysis of pi pi scattering
• Pion-nucleon scattering in chiral perturbation theory I: Isospin-symmetric case
• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
• Pion-nucleon scattering inside the Mandelstam triangle
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Regge analysis of the pi pi scattering amplitude
• Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
• Pion-nucleon scattering in chiral perturbation theory II: Fourth order calculation
• Low energy analysis of pi N --> pi N
• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• Roy-Steiner equations for gamma gamma -> pi pi
• Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian
• Size of the neutralino--nucleon cross--section in the light of a new determination of the pion--nucleon sigma term
• Analysis and interpretation of new low-energy Pi-Pi scattering data
• Couplings of light I=0 scalar mesons to simple operators in the complex plane
• Scalar form factors of light mesons
• Pionic deuterium
• Comparison of Pion-Kaon Scattering in SU(3) Chiral Perturbation Theory and Dispersion Relations
• On the analysis of the pion--nucleon $\sigma$--term: The size of the remainder at the Cheng--Dashen point
• Quark mass dependence of the pion vector form factor
• Partial wave analysiss of pbar-p -> piminus-piplus, pizero-pizero, eta-eta and eta-etaprime
• One-channel Roy equations revisited
• The role of the input in Roy's equations for pion-pion scattering
• Backward pion-nucleon scattering
• Forward analysis of $\pi$N scattering with an expansion method

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